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## Homework Statement

[tex]y' + 2ty = t^3[/tex]

## Homework Equations

Integrating factors and variation of parameters

## The Attempt at a Solution

Ive solved for m

[tex] M = e^{\int 2t\,dx} [/tex]

[tex] M = e^t^2 [/tex] (this is e^t^2, but doesnt look like it in latex)

I multiplied both sides by M

[tex](e^t^2)(y') + (e^t^2)(2ty) = (e^t^2)(t^3)[/tex]

The part im having trouble with is the next step. Im suppost to find a function so when you take the derivative of that function, it is the same as the left hand side of this problem, or [tex](e^t^2)(y') + (e^t^2)(2ty)[/tex]

Any suggestions? Is there a simple formula you can use that always works in these cases? It seems like ive tried [tex]\frac{d}{dt}(y)(e^t^2)[/tex] but it wont work.

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